9. EXEMPLES DE CALCUL DE STRUCTURES EN LAMIBOIS Déformation instantanée w_inst = w_(inst,g) + w_(inst,q) w_(inst,g)=(5〖∙g〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+〖〖6/5∙g〗_(d, (4.74) w_(inst,g)=1,30 mm+0,49 mm=1,79 mm w_(inst,q)=(5〖∙q〗_(d,SLS)∙s∙L^4)/(〖384∙E〗_mean∙I)+(6/5∙〖q_(d,SLS)∙s∙L〗 mm+1,08 mm=3,95 mm w_inst=1,79 mm+3,95 mm=5,5 mm Déformation finale w_(net,fin) = (1+k_def)∙w_(inst,g) + (1+ψ_2∙k_def)∙w_(inst,q) (4.73) Remarque : Pour la charge due à la neige dans l’Annexe Nationale finlandaise : ψ2 = 0,2. w_(net,fin) = (1+0,6)∙1,79 mm + (1+0,2∙0,6)∙3,95 mm = 7,3 mm Lorsque l’exigence est w_(net,fin)≤L/300=2300/300=7,7 mm→OK La poutre de linteau répond aux exigences de conception. Cependant, dans la pratique, les longueurs de’support requises sont assez importantes et, pour les fenêtres, une limite de déformation plus stricte peut être exigée. Par conséquent, un linteau double 2x45x260 mm ou un linteau 69x300 mm en LVL 36 C pourrait être un choix plus approprié. c,90,d = c,90,d ef = c,90,d ∙� support+15 mm� (4.14) c,90,d = 25,6kN 45mm∙ (150mm + 15mm) = 3,4 N/mm2 c,90 ∙ c,90,edge,d = c,90 ∙ mod M ∙ c,90,edge,k =1,0∙ 0 1 , , 8 2∙ 6 N/mm2 = 4 N/mm2 c,90,d ≤ c,90 ∙ m,0,edge,d →OK (4.13) inst = inst,g + inst,q inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5∙ d,SLS ∙ ∙ 2 8∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) net,fin = (1+0,6)∙ 1,79 mm + (1 + 0,2∙ 0,6)∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 =2 3 3 0 0 0 0 = 7,7 mm→OK inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5∙ d,SLS ∙ ∙ 4 384∙ mean ∙ + 6/5∙ d,SLS ∙ ∙ 2 8∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) net,fin = (1+0,6)∙ 1,79 mm + (1 + 0,2∙ 0,6)∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 =2 3 3 0 0 0 0 = 7,7 mm→OK Vérification des ELS 223 (255) inst,g =5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 1,30 mm+ 0,49 mm = 1,79 mm inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm Final deflection net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) Note: For the snow load in Finnish National annex: ψ2 = 0,2 net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 , 2303000mm= 7,7 mm → OK The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a more suitable choice. 9.3 Double LVL 48 P ridge beam for roof Single-span ridge beam of the roof in a one family house is LVL 48 P double beam 2x51x400 mm. Span length is L = 4000 mm, width of the loading area 6000 mm and roof rafters connected to the sides of the beam at spacing s = 1200 mm. Support length is 120 mm. Snow load sk is 2,5 kN/m2, own weight of the roof structure is 1,0 kN/m2 and own weigh of the beam is 0,2 kN/m. Service class SC1. Beam properties: Bending strength edgewise fm,0,edge,k = 44 N/mm2 Shear strength edgewise fv,0,edge,k = 4,2 N/mm2 Compression perpendicular to grain edgewise fc,90,edge,k = 6 N/mm2 Modulus of elasticity E0,k = 11 600 N/mm2 Modulus of elasticity E0,mean = 13 800 N/mm2 Modulus of rigidity G0,edge,k = 600 N/mm2 222 (253) inst,g 5∙ d,SLS∙ ∙ 4 384∙ mean∙ + 6 5∙ d,SLS∙ ∙ 2 8∙ mean (4.74) inst,g = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 1,30 mm+ 0,49 mm = 1,79 mm inst,g = 1,30 mm + 0,49 mm = 1,79 mm inst,q = 5 ∙ d,SLS ∙ ∙ 4 384 ∙ mean ∙ + 6/5 ∙ d,SLS ∙ ∙ 2 8 ∙ mean = 2,87 mm+ 1,08 mm = 3,95 mm = 1,79 mm + 3,95 mm = 5,5 mm Final deflection net,fin = (1+ def) ∙ inst,g + (1+ 2 ∙ def) ∙ inst,q (4.73) Note: For the snow load in Finnish National annex: ψ2 = 0,2 net,fin = (1 + 0,6) ∙ 1,79 mm + (1 + 0,2 ∙ 0,6) ∙ 3,95 mm = 7,3 mm When the requirement is net,fin ≤3 L 00 , 2 3 3 0 0 0 0 = 7,7 mm → OK The lintel beam fulfils the design requirements. However, in practice the required support lengths are quite long and for windows a more strict deflection limit can be required. Therefore a double lintel 2x45x260 mm or a 69x300 mm lintel from LVL 36 C could be a more suitable choice. 9.3 Double LVL 48 P ridge beam for roof Single-span ridge beam of the roof in a one family house is LVL 48 P double beam 2x51x400 mm. Span length is L = 4000 mm, width of the loading area 6000 mm and roof rafters connected to the sides of the beam at spacing s = 1200 mm. Support length is 120 mm. Snow load sk is 2,5 kN/m2, own weight of the roof structure is 1,0 kN/m2 and own weigh of the beam is 0,2 kN/m. Beam properties: Bending strength edgewise fm,0,edge,k = 44 N/mm2 Shear strength edgewise fv,0,edge,k = 4,2 N/mm2 Compression perpendicular to grain edgewise fc,90,edge,k = 6 N/mm2 Modulus of elasticity E0,k = 11 600 N/mm2 Modulus of elasticity E0,mean = 13 800 N/mm2 Modulus of rigidity G0,edge,k = 600 N/mm2 Modulus of rigidity G0,edge,mean = 400 N/mm2 ELS ELS ELS ELS Manuel sur le Lamibois (LVL) – Europe 187
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